INELASTIC INTERACTIONS OF SOLITARY WAVE SOLUTIONS OF THE EQUAL WIDTH WAVE EQUATION

摘要

The equal width (EW) wave equation is a model partial diu000berential equation for thernsimulation of one-dimensional wave propagation in media with nonlinear wave steepeningrnand dispersion processes. The EW equation is solved by using an advanced numericalrnmethod of lines with an adaptive grid whose node movement is based on an equidistribu-rntion principle. The solution procedure is described and the performance of the solutionrnmethod is assessed by means of computed solutions and error measures. The interactionsrnof two solitary waves, such as two waves that collide or one wave that overtakes a slowerrnwave are studied numerically. It is shown that the transmitted waves may retain muchrnof their original shapes and speeds after the interaction and additional waves can be gen-rnerated by the inelastic interaction process. It is also shown that the head-on collision ofrntwo solitary waves produces a train of non-negligible amplitude waves moving betweenrnthe transmitted waves, and the collision also produces a strong stationary disturbancernwith very steep gradients and curvatures.